This is a English version of the original guide and I am not very good at English so some of the sentences may seem strange to read. Sorry for this. You can leave a message below if I have any grammatical mistakes.

Anyway, this guide is inspired by Valve’s record method for the discovery of lambda caches (achievement Lambda Locators) in Half-Life 2.

In Half-Life 2, an achievement named Lambda Locator requires players to find all supplies in separate lambda caches. Valve use a string of Boolean values in gamestate.txt to record the progress on that achievement. And Black Mesa have a similar method for Prolific Popper achievement. In Black Mesa, the file path is
***\SteamLibrary\steamapps\common\Black Mesa\bms\gamestate.txt
One line in the file looks like this:
The exact location of the line depends on your game progress, but there should be only one line contained text looked like this. It’s easy to find out that 0xFFFFFFFFFFFFFFFF is a hexadecimal number. If we convert it to binary, then it will be sixty-four numbers 1. Sixty-four numbers represent sixty-four bubbles. Protozoans according to achievement description, but they do look like bubbles ;D Every number is Boolean type, and has two possible values, which are 1 and 0, aka true and false. A bubble that has been shot is a 1, while a bubble has never been shot is a 0. So the string above means you have already done all the job, after which this line should appear in the 26th section of the text file.

It should be noted that the counting is not in regular order, instead, the string is reversed, so that the first (leftmost) number actually represents the 64th bubble.
A simple example: If the string is 0xFFFFFFFDFFFFFFFF, you can tell that the 31st number (from left to right) is 0, but it means the 34th bubble hasn’t been shot. The correct way to read the string is from right to left.

The video is a full run for the achievement and the guide shows a convenient way to get to where you want to be.

https://www.youtube.com/watch?v=9MYOCmdOlL4

https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=1920599249

Here is a cheating way to get the achievement quickly. I haven’t test it in Black Mesa so I don’t know whether it really can work or not. I do know it works in Half-Life 2, as HL2 is essentially identical to Black Mesa so theoretically it works.
You can modify the string to trick the game.
A simple example: First, Change the string to 0xFFFFFFFFFFFFFFFE. Then load the game and shoot the first bubble. You should earn the achievement after that. Modify other number should be okay as well, since this is just the simplest way.
Be aware that directly change the string to 0xFFFFFFFFFFFFFFFF will NOT do the job, you have to shoot a bubble to trigger the string check. Plus, the text file won’t include all the sections until you've completed the game once, so the string location in the file will change too. You may not be able to get the achievement through this method and bugs may occur in this case.

A big THANK YOU to Black Mesa and Half-Life community, especially guide producers.

I am just a knowledge porter, without previous community contributors I definitely can’t find this.

All your likes and favourites and Steam Points awards means a lot to me. I really hope this guide helped you!